As stated before, Bayesian modelling requires the specification of a prior distribution \(\pi (\omega , \theta )\) . We assume prior independence between \(\omega \)  and \(\theta \)  and, consequently \(\pi (\omega , \theta )= \pi (\omega ) \pi (\theta )\) . We propose to consider non-informative uniform prior distributions for \(\theta \) , as they will produce a minimal influence on the inference. For \(\omega \) , we decided to use a non-informative symmetric Dirichlet distribution called Perks' prior (see [1]} and supplemental material).
